4-acid digestion is even stronger than aqua regia digest. It is...

4-acid digestion is even stronger than aqua regia digest. It is a combination of sulphuric, hydrochloric, nitric and hydrofluoric acid. The sample is then digested (boiled at a very high temperature) for something like 2 hours. The "resistive REE minerals" they refer to are typically encased in quartz (which is one of the few minerals that doesn't leach well in 4-acid digest) or quartz-like minerals, so they do a fusion with some chemicals in a furnace and then follow up with the 4-acid digest.

These samples are hungrier for acid than Keith Richards on a bender.